The classicality concept is formulated. It is used to derive Wigner inequalities dependent on three instants. The possibility of testing experimentally violations of these inequalities in pure and mixed flavor states of a pair of neutral pseudoscalar mesons is studied. Within the Werner background model, it is shown that a violation of time-dependent Wigner inequalities may be observed even at a 50
% fraction of background processes.
We examine the feasibility of the Bell test (i.e., detecting a violation of the Bell inequality) with the ATLAS detector at the Large Hadron Collider (LHC) at CERN through the flavor entanglement between the
B mesons. After addressing the possible issues that arise associated with the experiment and how they may be treated based on an analogy with conventional Bell tests, we show in our simulation study that under realistic conditions (expected from the LHC Run 3 operation) that the Bell test is feasible under mild assumptions. The definitive factor for this promising result lies primarily in the fact that the ATLAS detector is capable of measuring the decay times of the
B mesons independently, which was not possible in the previous experiment with the Belle detector at KEK. This result suggests the possibility of the Bell test in much higher energy domains and may open up a new arena for experimental studies of quantum foundations.
In this study, we introduce the concept of Classicality and derive Wigner inequalities that depend on two instants, with a potential extension to three instants. We explore the experimental feasibility of testing the violations of these inequalities in both pure and mixed flavor states of
K0-,
D0-, and
Bs- meson pairs. Using the Werner noise model, we demonstrate that violations of time-dependent Wigner inequalities can be detected even when background processes constitute up to 50% of the system.